Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4593478 | Journal of Number Theory | 2015 | 8 Pages |
Abstract
For any a∈(0,∞)a∈(0,∞), we prove the strict concavity of the functionηa(t):=∑m=0∞(−1)m(am+1)t on (0,∞)(0,∞), and provide fast computations of their derivatives on (0,∞)(0,∞). We give short proofs mainly based on differentiation formulas concerning the gamma process. In particular, our results apply to Dirichlet's eta and beta functions η1(t)η1(t) and η2(t)η2(t), respectively.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
José A. Adell, Alberto Lekuona,